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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 23 Nov 2008 08:00:12 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/23/t12274524635lxohs4wh0lg1dv.htm/, Retrieved Sun, 19 May 2024 12:16:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25281, Retrieved Sun, 19 May 2024 12:16:54 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

192

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Multiple Regression] [] [2007-11-19 20:22:41] [3a1956effdcb54c39e5044435310d6c8]
-    D  [Multiple Regression] [seatbelt_3.2.] [2008-11-23 14:44:53] [922d8ae7bd2fd460a62d9020ccd4931a]
F   PD      [Multiple Regression] [seatbelt3CG2] [2008-11-23 15:00:12] [89a49ebb3ece8e9a225c7f9f53a14c57] [Current]
-   PD        [Multiple Regression] [dummy] [2008-12-07 12:19:24] [922d8ae7bd2fd460a62d9020ccd4931a] 
-    D          [Multiple Regression] [dummy3] [2008-12-11 14:24:38] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RMPD            [Standard Deviation-Mean Plot] [lambda] [2008-12-11 16:25:56] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RM D              [Variance Reduction Matrix] [denD] [2008-12-11 16:30:20] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RMP                 [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-11 16:35:54] [922d8ae7bd2fd460a62d9020ccd4931a] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelation2] [2008-12-11 16:40:41] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RMP                     [Spectral Analysis] [spectrum] [2008-12-11 16:45:17] [922d8ae7bd2fd460a62d9020ccd4931a] 
-   P                       [Spectral Analysis] [spectrum2] [2008-12-11 16:48:27] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RMP                         [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-11 17:56:59] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RMP                           [ARIMA Backward Selection] [ARMAproces] [2008-12-11 18:10:55] [922d8ae7bd2fd460a62d9020ccd4931a] 
- RMP                             [ARIMA Forecasting] [ARIMAforecasting] [2008-12-11 18:25:54] [922d8ae7bd2fd460a62d9020ccd4931a] 
-   PD        [Multiple Regression] [dummy2] [2008-12-07 12:43:57] [922d8ae7bd2fd460a62d9020ccd4931a] 
-   PD        [Multiple Regression] [dummy3] [2008-12-07 12:55:51] [922d8ae7bd2fd460a62d9020ccd4931a] 
-   PD        [Multiple Regression] [dummy4] [2008-12-07 13:11:11] [922d8ae7bd2fd460a62d9020ccd4931a] 

Feedback Forum

2008-11-29 15:20:54 [Thomas Plasschaert] [reply] 
goede interpretatie en berekeningen, juiste conclusies getrokken, verder geen toevoegingen nodig
2008-11-30 13:21:31 [6066575aa30c0611e452e930b1dff53d] [reply] 
Bij deze vraag werd de financiële crisis als dummy variabele genomen en de cijfers die gebruikt werden waren de indexcijfers voor de productie van consumptiegoederen. Uit de multiple linear regression-estimated regression equation werd de juiste conclusie getrokken dat als er een financiële crisis is, de productie van consumptiegoederen daalt met 4 per maand. Bij de multiple linear regression - ordinary least squares werd juist besloten dat er geen significant verschil is en dat we het effect van onze gebeurtenis aan het toeval kunnen toeschrijven. De nulhypothese werd dus aanvaard. Verder is men nog vergeten te vermelden dat op de lange termijn de productie van consumptiegoederen gemiddeld stijgt met 0.28. Uit de tabel van multiple linear regression-regression statistics werd juist besloten dat we 73% van de schommelingen die ontstaan door de gebeurtenis kunnen verklaren. Men is wel vergeten te vermelden dat de residuele standaardfout 5 bedraagt. Dit is de te verwachten fout die ik maak voor mijn residu's. Bij de grafiek van de actuals and interpolation zien we een positief stijgende trend en na ongeveer 75 (op de x-as) slaat deze trend om in een negatieve trend. Bij de grafiek van de residuals werd er duidelijk besloten dat het gemiddelde van de voorspellingsfouten niet constant zijn en niet gelijk zijn aan nul. Bij de residual histogram werd ook duidelijk vermeld dat er aan beide kanten nog een scheve verdeling te zien is. Bij de residual density plot zie je duidelijk een inzakking aan de linkerkant. Bij de residual normal Q-Qplot is men vergeten te vermelden dat deze redelijk goed aansluit bij een rechte. Bij de residual lag plot, lowess, and regression line werd duidelijk vermeld dat het gaat om een negatieve correlatie. Uit de residual autocorrelation function werd het juiste besluit genomen dat aan de assumptie van geen patroon of geen autocorrelatie voldaan is. 
  2008-12-01 18:49:08 [6066575aa30c0611e452e930b1dff53d] [reply] 
Het klopt niet dat er geen sprake is van autocorrelatie. Uit de residual autocorrelation function kunnen we immers afleiden dat er wel sprake is van autocorrelatie. Dus aan de assumptie dat er geen patroon of geen autocorrelatie mag zijn is dus niet voldaan. 
2008-12-01 11:59:47 [Jessica Alves Pires] [reply] 
Ik vind dat de grafieken bij deze berekening (met linear trend en met dummies) goed geïnterpreteerd zijn. Ik vind het wel spijtig dat de student geen vergelijking maakt met de berekening zonder linear trend en zonder dummies. De student had bijvoorbeeld kunnen zeggen dat de standdaardfout daalt van 9.48213286856506 naar 5.00612210608242 met invoering van dummies en linear trend. Of dat de R-squared gestegen is van 0.066921912517871 naar 0.777520986287843. Men krijgt dus een nauwkeuriger voorspelling met de invoering van dummies en linear trend. Ook hadden de volgende regressie assumpties vermeld  mogen worden: de verdeling moet normaal verdeeld zijn en de onzekerheid, dus de spreiding moet constant zijn.

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25281&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25281&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation
Consumptiegoederen[t] = + 92.5783032666992 -4.01552901023891`Wel(1)_geen(0)_financi�le_crisis`[t] + 1.73044145132453M1[t] + 17.8169165447749M2[t] + 19.5892887615797M3[t] + 12.6330895498131M4[t] + 11.3054617666179M5[t] + 5.14926255485129M6[t] + 3.65020620022753M7[t] + 15.1797212741752M8[t] + 5.93780777669429M9[t] + 3.66732285064196M10[t] + 13.8682664960182M11[t] + 0.284770640338047t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Consumptiegoederen[t] =  +  92.5783032666992 -4.01552901023891`Wel(1)_geen(0)_financi�le_crisis`[t] +  1.73044145132453M1[t] +  17.8169165447749M2[t] +  19.5892887615797M3[t] +  12.6330895498131M4[t] +  11.3054617666179M5[t] +  5.14926255485129M6[t] +  3.65020620022753M7[t] +  15.1797212741752M8[t] +  5.93780777669429M9[t] +  3.66732285064196M10[t] +  13.8682664960182M11[t] +  0.284770640338047t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25281&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Consumptiegoederen[t] =  +  92.5783032666992 -4.01552901023891`Wel(1)_geen(0)_financi�le_crisis`[t] +  1.73044145132453M1[t] +  17.8169165447749M2[t] +  19.5892887615797M3[t] +  12.6330895498131M4[t] +  11.3054617666179M5[t] +  5.14926255485129M6[t] +  3.65020620022753M7[t] +  15.1797212741752M8[t] +  5.93780777669429M9[t] +  3.66732285064196M10[t] +  13.8682664960182M11[t] +  0.284770640338047t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25281&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
Consumptiegoederen[t] = + 92.5783032666992 -4.01552901023891`Wel(1)_geen(0)_financi�le_crisis`[t] + 1.73044145132453M1[t] + 17.8169165447749M2[t] + 19.5892887615797M3[t] + 12.6330895498131M4[t] + 11.3054617666179M5[t] + 5.14926255485129M6[t] + 3.65020620022753M7[t] + 15.1797212741752M8[t] + 5.93780777669429M9[t] + 3.66732285064196M10[t] + 13.8682664960182M11[t] + 0.284770640338047t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	92.5783032666992	2.20249	42.0335	0	0
`Wel(1)_geen(0)_financi�le_crisis`	-4.01552901023891	1.934446	-2.0758	0.041535	0.020767
M1	1.73044145132453	2.593436	0.6672	0.506782	0.253391
M2	17.8169165447749	2.686586	6.6318	0	0
M3	19.5892887615797	2.685509	7.2944	0	0
M4	12.6330895498131	2.684749	4.7055	1.2e-05	6e-06
M5	11.3054617666179	2.684308	4.2117	7.3e-05	3.7e-05
M6	5.14926255485129	2.684184	1.9184	0.059085	0.029543
M7	3.65020620022753	2.684379	1.3598	0.178197	0.089099
M8	15.1797212741752	2.684891	5.6538	0	0
M9	5.93780777669429	2.685722	2.2109	0.030267	0.015133
M10	3.66732285064196	2.68687	1.3649	0.176593	0.088296
M11	13.8682664960182	2.688335	5.1587	2e-06	1e-06
t	0.284770640338047	0.029221	9.7455	0	0

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 92.5783032666992 & 2.20249 & 42.0335 & 0 & 0 \tabularnewline
`Wel(1)_geen(0)_financi�le_crisis` & -4.01552901023891 & 1.934446 & -2.0758 & 0.041535 & 0.020767 \tabularnewline
M1 & 1.73044145132453 & 2.593436 & 0.6672 & 0.506782 & 0.253391 \tabularnewline
M2 & 17.8169165447749 & 2.686586 & 6.6318 & 0 & 0 \tabularnewline
M3 & 19.5892887615797 & 2.685509 & 7.2944 & 0 & 0 \tabularnewline
M4 & 12.6330895498131 & 2.684749 & 4.7055 & 1.2e-05 & 6e-06 \tabularnewline
M5 & 11.3054617666179 & 2.684308 & 4.2117 & 7.3e-05 & 3.7e-05 \tabularnewline
M6 & 5.14926255485129 & 2.684184 & 1.9184 & 0.059085 & 0.029543 \tabularnewline
M7 & 3.65020620022753 & 2.684379 & 1.3598 & 0.178197 & 0.089099 \tabularnewline
M8 & 15.1797212741752 & 2.684891 & 5.6538 & 0 & 0 \tabularnewline
M9 & 5.93780777669429 & 2.685722 & 2.2109 & 0.030267 & 0.015133 \tabularnewline
M10 & 3.66732285064196 & 2.68687 & 1.3649 & 0.176593 & 0.088296 \tabularnewline
M11 & 13.8682664960182 & 2.688335 & 5.1587 & 2e-06 & 1e-06 \tabularnewline
t & 0.284770640338047 & 0.029221 & 9.7455 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25281&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]92.5783032666992[/C][C]2.20249[/C][C]42.0335[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Wel(1)_geen(0)_financi�le_crisis`[/C][C]-4.01552901023891[/C][C]1.934446[/C][C]-2.0758[/C][C]0.041535[/C][C]0.020767[/C][/ROW]
[ROW][C]M1[/C][C]1.73044145132453[/C][C]2.593436[/C][C]0.6672[/C][C]0.506782[/C][C]0.253391[/C][/ROW]
[ROW][C]M2[/C][C]17.8169165447749[/C][C]2.686586[/C][C]6.6318[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]19.5892887615797[/C][C]2.685509[/C][C]7.2944[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]12.6330895498131[/C][C]2.684749[/C][C]4.7055[/C][C]1.2e-05[/C][C]6e-06[/C][/ROW]
[ROW][C]M5[/C][C]11.3054617666179[/C][C]2.684308[/C][C]4.2117[/C][C]7.3e-05[/C][C]3.7e-05[/C][/ROW]
[ROW][C]M6[/C][C]5.14926255485129[/C][C]2.684184[/C][C]1.9184[/C][C]0.059085[/C][C]0.029543[/C][/ROW]
[ROW][C]M7[/C][C]3.65020620022753[/C][C]2.684379[/C][C]1.3598[/C][C]0.178197[/C][C]0.089099[/C][/ROW]
[ROW][C]M8[/C][C]15.1797212741752[/C][C]2.684891[/C][C]5.6538[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]5.93780777669429[/C][C]2.685722[/C][C]2.2109[/C][C]0.030267[/C][C]0.015133[/C][/ROW]
[ROW][C]M10[/C][C]3.66732285064196[/C][C]2.68687[/C][C]1.3649[/C][C]0.176593[/C][C]0.088296[/C][/ROW]
[ROW][C]M11[/C][C]13.8682664960182[/C][C]2.688335[/C][C]5.1587[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]t[/C][C]0.284770640338047[/C][C]0.029221[/C][C]9.7455[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25281&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25281&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	92.5783032666992	2.20249	42.0335	0	0
`Wel(1)_geen(0)_financi�le_crisis`	-4.01552901023891	1.934446	-2.0758	0.041535	0.020767
M1	1.73044145132453	2.593436	0.6672	0.506782	0.253391
M2	17.8169165447749	2.686586	6.6318	0	0
M3	19.5892887615797	2.685509	7.2944	0	0
M4	12.6330895498131	2.684749	4.7055	1.2e-05	6e-06
M5	11.3054617666179	2.684308	4.2117	7.3e-05	3.7e-05
M6	5.14926255485129	2.684184	1.9184	0.059085	0.029543
M7	3.65020620022753	2.684379	1.3598	0.178197	0.089099
M8	15.1797212741752	2.684891	5.6538	0	0
M9	5.93780777669429	2.685722	2.2109	0.030267	0.015133
M10	3.66732285064196	2.68687	1.3649	0.176593	0.088296
M11	13.8682664960182	2.688335	5.1587	2e-06	1e-06
t	0.284770640338047	0.029221	9.7455	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.881771504579187
R-squared	0.777520986287843
Adjusted R-squared	0.73678539222787
F-TEST (value)	19.0870172445048
F-TEST (DF numerator)	13
F-TEST (DF denominator)	71
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.00612210608242
Sum Squared Residuals	1779.34935641150

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.881771504579187 \tabularnewline
R-squared & 0.777520986287843 \tabularnewline
Adjusted R-squared & 0.73678539222787 \tabularnewline
F-TEST (value) & 19.0870172445048 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 71 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.00612210608242 \tabularnewline
Sum Squared Residuals & 1779.34935641150 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25281&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.881771504579187[/C][/ROW]
[ROW][C]R-squared[/C][C]0.777520986287843[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.73678539222787[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]19.0870172445048[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]71[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.00612210608242[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1779.34935641150[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25281&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25281&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R	0.881771504579187
R-squared	0.777520986287843
Adjusted R-squared	0.73678539222787
F-TEST (value)	19.0870172445048
F-TEST (DF numerator)	13
F-TEST (DF denominator)	71
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.00612210608242
Sum Squared Residuals	1779.34935641150

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	97.8	94.593515358362	3.20648464163802
2	107.4	110.964761092150	-3.56476109215017
3	117.5	113.021903949293	4.47809605070698
4	105.6	106.350475377864	-0.750475377864452
5	97.4	105.307618235007	-7.9076182350073
6	99.5	99.4361896635787	0.0638103364212654
7	98	98.221903949293	-0.221903949293019
8	104.3	110.036189663579	-5.73618966357873
9	100.6	101.079046806436	-0.479046806435882
10	101.1	99.0933325207216	2.00666747927841
11	103.9	109.579046806436	-5.67904680643587
12	96.9	95.9955509507557	0.904449049244283
13	95.5	98.0107630424183	-2.51076304241829
14	108.4	114.382008776207	-5.98200877620671
15	117	116.439151633350	0.560848366650421
16	103.8	109.767723061921	-5.96772306192101
17	100.8	108.724865919064	-7.92486591906387
18	110.6	102.853437347635	7.7465626523647
19	104	101.639151633350	2.36084836665042
20	112.6	113.453437347635	-0.8534373476353
21	107.3	104.496294490492	2.80370550950756
22	98.9	102.510580204778	-3.61058020477815
23	109.8	112.996294490492	-3.19629449049244
24	104.9	99.4127986348123	5.48720136518773
25	102.2	101.428010726475	0.771989273525143
26	123.9	117.799256460263	6.10074353973672
27	124.9	119.856399317406	5.04360068259387
28	112.7	113.184970745978	-0.484970745977566
29	121.9	112.142113603120	9.75788639687958
30	100.6	106.270685031692	-5.67068503169186
31	104.3	105.056399317406	-0.756399317406144
32	120.4	116.870685031692	3.52931496830816
33	107.5	107.913542174549	-0.413542174548996
34	102.9	105.927827888835	-3.02782788883471
35	125.6	116.413542174549	9.186457825451
36	107.5	102.830046318869	4.66995368113116
37	108.8	104.845258410531	3.95474158946858
38	128.4	121.216504144320	7.18349585568016
39	121.1	123.273647001463	-2.17364700146271
40	119.5	116.602218430034	2.89778156996587
41	128.7	115.559361287177	13.140638712823
42	108.7	109.687932715748	-0.987932715748414
43	105.5	108.473647001463	-2.9736470014627
44	119.8	120.287932715748	-0.487932715748415
45	111.3	111.330789858606	-0.0307898586055590
46	110.6	109.345075572891	1.25492442710872
47	120.1	119.830789858606	0.269210141394436
48	97.5	106.247294002925	-8.7472940029254
49	107.7	108.262506094588	-0.562506094587979
50	127.3	124.633751828376	2.66624817162359
51	117.2	126.690894685519	-9.49089468551926
52	119.8	120.019466114091	-0.219466114090695
53	116.2	118.976608971234	-2.77660897123355
54	111	113.105180399805	-2.10518039980498
55	112.4	111.890894685519	0.509105314480739
56	130.6	123.705180399805	6.89481960019502
57	109.1	114.748037542662	-5.64803754266212
58	118.8	112.762323256948	6.03767674305216
59	123.9	123.248037542662	0.651962457337885
60	101.6	109.664541686982	-8.06454168698197
61	112.8	111.679753778645	1.12024622135546
62	128	128.050999512433	-0.0509995124329651
63	129.6	130.108142369576	-0.508142369575828
64	125.8	123.436713798147	2.36328620185275
65	119.5	122.39385665529	-2.89385665529010
66	115.7	116.522428083862	-0.822428083861532
67	113.6	115.308142369576	-1.70814236957582
68	129.7	127.122428083862	2.57757191613846
69	112	118.165285226719	-6.16528522671867
70	116.8	116.179570941004	0.620429058995612
71	127	126.665285226719	0.334714773281321
72	112.1	109.066260360800	3.03373963920038
73	114.2	111.081472452462	3.11852754753782
74	121.1	127.452718186251	-6.35271818625062
75	131.6	129.509861043393	2.09013895660653
76	125	122.838432471965	2.1615675280351
77	120.4	121.795575329108	-1.39557532910775
78	117.7	115.924146757679	1.77585324232082
79	117.5	114.709861043393	2.79013895660653
80	120.6	126.524146757679	-5.92414675767919
81	127.5	117.567003900536	9.93299609946367
82	112.3	115.581289614822	-3.28128961482205
83	124.5	126.067003900536	-1.56700390053633
84	115.2	112.483508044856	2.71649195514383
85	105.4	114.498720136519	-9.09872013651875

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 97.8 & 94.593515358362 & 3.20648464163802 \tabularnewline
2 & 107.4 & 110.964761092150 & -3.56476109215017 \tabularnewline
3 & 117.5 & 113.021903949293 & 4.47809605070698 \tabularnewline
4 & 105.6 & 106.350475377864 & -0.750475377864452 \tabularnewline
5 & 97.4 & 105.307618235007 & -7.9076182350073 \tabularnewline
6 & 99.5 & 99.4361896635787 & 0.0638103364212654 \tabularnewline
7 & 98 & 98.221903949293 & -0.221903949293019 \tabularnewline
8 & 104.3 & 110.036189663579 & -5.73618966357873 \tabularnewline
9 & 100.6 & 101.079046806436 & -0.479046806435882 \tabularnewline
10 & 101.1 & 99.0933325207216 & 2.00666747927841 \tabularnewline
11 & 103.9 & 109.579046806436 & -5.67904680643587 \tabularnewline
12 & 96.9 & 95.9955509507557 & 0.904449049244283 \tabularnewline
13 & 95.5 & 98.0107630424183 & -2.51076304241829 \tabularnewline
14 & 108.4 & 114.382008776207 & -5.98200877620671 \tabularnewline
15 & 117 & 116.439151633350 & 0.560848366650421 \tabularnewline
16 & 103.8 & 109.767723061921 & -5.96772306192101 \tabularnewline
17 & 100.8 & 108.724865919064 & -7.92486591906387 \tabularnewline
18 & 110.6 & 102.853437347635 & 7.7465626523647 \tabularnewline
19 & 104 & 101.639151633350 & 2.36084836665042 \tabularnewline
20 & 112.6 & 113.453437347635 & -0.8534373476353 \tabularnewline
21 & 107.3 & 104.496294490492 & 2.80370550950756 \tabularnewline
22 & 98.9 & 102.510580204778 & -3.61058020477815 \tabularnewline
23 & 109.8 & 112.996294490492 & -3.19629449049244 \tabularnewline
24 & 104.9 & 99.4127986348123 & 5.48720136518773 \tabularnewline
25 & 102.2 & 101.428010726475 & 0.771989273525143 \tabularnewline
26 & 123.9 & 117.799256460263 & 6.10074353973672 \tabularnewline
27 & 124.9 & 119.856399317406 & 5.04360068259387 \tabularnewline
28 & 112.7 & 113.184970745978 & -0.484970745977566 \tabularnewline
29 & 121.9 & 112.142113603120 & 9.75788639687958 \tabularnewline
30 & 100.6 & 106.270685031692 & -5.67068503169186 \tabularnewline
31 & 104.3 & 105.056399317406 & -0.756399317406144 \tabularnewline
32 & 120.4 & 116.870685031692 & 3.52931496830816 \tabularnewline
33 & 107.5 & 107.913542174549 & -0.413542174548996 \tabularnewline
34 & 102.9 & 105.927827888835 & -3.02782788883471 \tabularnewline
35 & 125.6 & 116.413542174549 & 9.186457825451 \tabularnewline
36 & 107.5 & 102.830046318869 & 4.66995368113116 \tabularnewline
37 & 108.8 & 104.845258410531 & 3.95474158946858 \tabularnewline
38 & 128.4 & 121.216504144320 & 7.18349585568016 \tabularnewline
39 & 121.1 & 123.273647001463 & -2.17364700146271 \tabularnewline
40 & 119.5 & 116.602218430034 & 2.89778156996587 \tabularnewline
41 & 128.7 & 115.559361287177 & 13.140638712823 \tabularnewline
42 & 108.7 & 109.687932715748 & -0.987932715748414 \tabularnewline
43 & 105.5 & 108.473647001463 & -2.9736470014627 \tabularnewline
44 & 119.8 & 120.287932715748 & -0.487932715748415 \tabularnewline
45 & 111.3 & 111.330789858606 & -0.0307898586055590 \tabularnewline
46 & 110.6 & 109.345075572891 & 1.25492442710872 \tabularnewline
47 & 120.1 & 119.830789858606 & 0.269210141394436 \tabularnewline
48 & 97.5 & 106.247294002925 & -8.7472940029254 \tabularnewline
49 & 107.7 & 108.262506094588 & -0.562506094587979 \tabularnewline
50 & 127.3 & 124.633751828376 & 2.66624817162359 \tabularnewline
51 & 117.2 & 126.690894685519 & -9.49089468551926 \tabularnewline
52 & 119.8 & 120.019466114091 & -0.219466114090695 \tabularnewline
53 & 116.2 & 118.976608971234 & -2.77660897123355 \tabularnewline
54 & 111 & 113.105180399805 & -2.10518039980498 \tabularnewline
55 & 112.4 & 111.890894685519 & 0.509105314480739 \tabularnewline
56 & 130.6 & 123.705180399805 & 6.89481960019502 \tabularnewline
57 & 109.1 & 114.748037542662 & -5.64803754266212 \tabularnewline
58 & 118.8 & 112.762323256948 & 6.03767674305216 \tabularnewline
59 & 123.9 & 123.248037542662 & 0.651962457337885 \tabularnewline
60 & 101.6 & 109.664541686982 & -8.06454168698197 \tabularnewline
61 & 112.8 & 111.679753778645 & 1.12024622135546 \tabularnewline
62 & 128 & 128.050999512433 & -0.0509995124329651 \tabularnewline
63 & 129.6 & 130.108142369576 & -0.508142369575828 \tabularnewline
64 & 125.8 & 123.436713798147 & 2.36328620185275 \tabularnewline
65 & 119.5 & 122.39385665529 & -2.89385665529010 \tabularnewline
66 & 115.7 & 116.522428083862 & -0.822428083861532 \tabularnewline
67 & 113.6 & 115.308142369576 & -1.70814236957582 \tabularnewline
68 & 129.7 & 127.122428083862 & 2.57757191613846 \tabularnewline
69 & 112 & 118.165285226719 & -6.16528522671867 \tabularnewline
70 & 116.8 & 116.179570941004 & 0.620429058995612 \tabularnewline
71 & 127 & 126.665285226719 & 0.334714773281321 \tabularnewline
72 & 112.1 & 109.066260360800 & 3.03373963920038 \tabularnewline
73 & 114.2 & 111.081472452462 & 3.11852754753782 \tabularnewline
74 & 121.1 & 127.452718186251 & -6.35271818625062 \tabularnewline
75 & 131.6 & 129.509861043393 & 2.09013895660653 \tabularnewline
76 & 125 & 122.838432471965 & 2.1615675280351 \tabularnewline
77 & 120.4 & 121.795575329108 & -1.39557532910775 \tabularnewline
78 & 117.7 & 115.924146757679 & 1.77585324232082 \tabularnewline
79 & 117.5 & 114.709861043393 & 2.79013895660653 \tabularnewline
80 & 120.6 & 126.524146757679 & -5.92414675767919 \tabularnewline
81 & 127.5 & 117.567003900536 & 9.93299609946367 \tabularnewline
82 & 112.3 & 115.581289614822 & -3.28128961482205 \tabularnewline
83 & 124.5 & 126.067003900536 & -1.56700390053633 \tabularnewline
84 & 115.2 & 112.483508044856 & 2.71649195514383 \tabularnewline
85 & 105.4 & 114.498720136519 & -9.09872013651875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25281&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]97.8[/C][C]94.593515358362[/C][C]3.20648464163802[/C][/ROW]
[ROW][C]2[/C][C]107.4[/C][C]110.964761092150[/C][C]-3.56476109215017[/C][/ROW]
[ROW][C]3[/C][C]117.5[/C][C]113.021903949293[/C][C]4.47809605070698[/C][/ROW]
[ROW][C]4[/C][C]105.6[/C][C]106.350475377864[/C][C]-0.750475377864452[/C][/ROW]
[ROW][C]5[/C][C]97.4[/C][C]105.307618235007[/C][C]-7.9076182350073[/C][/ROW]
[ROW][C]6[/C][C]99.5[/C][C]99.4361896635787[/C][C]0.0638103364212654[/C][/ROW]
[ROW][C]7[/C][C]98[/C][C]98.221903949293[/C][C]-0.221903949293019[/C][/ROW]
[ROW][C]8[/C][C]104.3[/C][C]110.036189663579[/C][C]-5.73618966357873[/C][/ROW]
[ROW][C]9[/C][C]100.6[/C][C]101.079046806436[/C][C]-0.479046806435882[/C][/ROW]
[ROW][C]10[/C][C]101.1[/C][C]99.0933325207216[/C][C]2.00666747927841[/C][/ROW]
[ROW][C]11[/C][C]103.9[/C][C]109.579046806436[/C][C]-5.67904680643587[/C][/ROW]
[ROW][C]12[/C][C]96.9[/C][C]95.9955509507557[/C][C]0.904449049244283[/C][/ROW]
[ROW][C]13[/C][C]95.5[/C][C]98.0107630424183[/C][C]-2.51076304241829[/C][/ROW]
[ROW][C]14[/C][C]108.4[/C][C]114.382008776207[/C][C]-5.98200877620671[/C][/ROW]
[ROW][C]15[/C][C]117[/C][C]116.439151633350[/C][C]0.560848366650421[/C][/ROW]
[ROW][C]16[/C][C]103.8[/C][C]109.767723061921[/C][C]-5.96772306192101[/C][/ROW]
[ROW][C]17[/C][C]100.8[/C][C]108.724865919064[/C][C]-7.92486591906387[/C][/ROW]
[ROW][C]18[/C][C]110.6[/C][C]102.853437347635[/C][C]7.7465626523647[/C][/ROW]
[ROW][C]19[/C][C]104[/C][C]101.639151633350[/C][C]2.36084836665042[/C][/ROW]
[ROW][C]20[/C][C]112.6[/C][C]113.453437347635[/C][C]-0.8534373476353[/C][/ROW]
[ROW][C]21[/C][C]107.3[/C][C]104.496294490492[/C][C]2.80370550950756[/C][/ROW]
[ROW][C]22[/C][C]98.9[/C][C]102.510580204778[/C][C]-3.61058020477815[/C][/ROW]
[ROW][C]23[/C][C]109.8[/C][C]112.996294490492[/C][C]-3.19629449049244[/C][/ROW]
[ROW][C]24[/C][C]104.9[/C][C]99.4127986348123[/C][C]5.48720136518773[/C][/ROW]
[ROW][C]25[/C][C]102.2[/C][C]101.428010726475[/C][C]0.771989273525143[/C][/ROW]
[ROW][C]26[/C][C]123.9[/C][C]117.799256460263[/C][C]6.10074353973672[/C][/ROW]
[ROW][C]27[/C][C]124.9[/C][C]119.856399317406[/C][C]5.04360068259387[/C][/ROW]
[ROW][C]28[/C][C]112.7[/C][C]113.184970745978[/C][C]-0.484970745977566[/C][/ROW]
[ROW][C]29[/C][C]121.9[/C][C]112.142113603120[/C][C]9.75788639687958[/C][/ROW]
[ROW][C]30[/C][C]100.6[/C][C]106.270685031692[/C][C]-5.67068503169186[/C][/ROW]
[ROW][C]31[/C][C]104.3[/C][C]105.056399317406[/C][C]-0.756399317406144[/C][/ROW]
[ROW][C]32[/C][C]120.4[/C][C]116.870685031692[/C][C]3.52931496830816[/C][/ROW]
[ROW][C]33[/C][C]107.5[/C][C]107.913542174549[/C][C]-0.413542174548996[/C][/ROW]
[ROW][C]34[/C][C]102.9[/C][C]105.927827888835[/C][C]-3.02782788883471[/C][/ROW]
[ROW][C]35[/C][C]125.6[/C][C]116.413542174549[/C][C]9.186457825451[/C][/ROW]
[ROW][C]36[/C][C]107.5[/C][C]102.830046318869[/C][C]4.66995368113116[/C][/ROW]
[ROW][C]37[/C][C]108.8[/C][C]104.845258410531[/C][C]3.95474158946858[/C][/ROW]
[ROW][C]38[/C][C]128.4[/C][C]121.216504144320[/C][C]7.18349585568016[/C][/ROW]
[ROW][C]39[/C][C]121.1[/C][C]123.273647001463[/C][C]-2.17364700146271[/C][/ROW]
[ROW][C]40[/C][C]119.5[/C][C]116.602218430034[/C][C]2.89778156996587[/C][/ROW]
[ROW][C]41[/C][C]128.7[/C][C]115.559361287177[/C][C]13.140638712823[/C][/ROW]
[ROW][C]42[/C][C]108.7[/C][C]109.687932715748[/C][C]-0.987932715748414[/C][/ROW]
[ROW][C]43[/C][C]105.5[/C][C]108.473647001463[/C][C]-2.9736470014627[/C][/ROW]
[ROW][C]44[/C][C]119.8[/C][C]120.287932715748[/C][C]-0.487932715748415[/C][/ROW]
[ROW][C]45[/C][C]111.3[/C][C]111.330789858606[/C][C]-0.0307898586055590[/C][/ROW]
[ROW][C]46[/C][C]110.6[/C][C]109.345075572891[/C][C]1.25492442710872[/C][/ROW]
[ROW][C]47[/C][C]120.1[/C][C]119.830789858606[/C][C]0.269210141394436[/C][/ROW]
[ROW][C]48[/C][C]97.5[/C][C]106.247294002925[/C][C]-8.7472940029254[/C][/ROW]
[ROW][C]49[/C][C]107.7[/C][C]108.262506094588[/C][C]-0.562506094587979[/C][/ROW]
[ROW][C]50[/C][C]127.3[/C][C]124.633751828376[/C][C]2.66624817162359[/C][/ROW]
[ROW][C]51[/C][C]117.2[/C][C]126.690894685519[/C][C]-9.49089468551926[/C][/ROW]
[ROW][C]52[/C][C]119.8[/C][C]120.019466114091[/C][C]-0.219466114090695[/C][/ROW]
[ROW][C]53[/C][C]116.2[/C][C]118.976608971234[/C][C]-2.77660897123355[/C][/ROW]
[ROW][C]54[/C][C]111[/C][C]113.105180399805[/C][C]-2.10518039980498[/C][/ROW]
[ROW][C]55[/C][C]112.4[/C][C]111.890894685519[/C][C]0.509105314480739[/C][/ROW]
[ROW][C]56[/C][C]130.6[/C][C]123.705180399805[/C][C]6.89481960019502[/C][/ROW]
[ROW][C]57[/C][C]109.1[/C][C]114.748037542662[/C][C]-5.64803754266212[/C][/ROW]
[ROW][C]58[/C][C]118.8[/C][C]112.762323256948[/C][C]6.03767674305216[/C][/ROW]
[ROW][C]59[/C][C]123.9[/C][C]123.248037542662[/C][C]0.651962457337885[/C][/ROW]
[ROW][C]60[/C][C]101.6[/C][C]109.664541686982[/C][C]-8.06454168698197[/C][/ROW]
[ROW][C]61[/C][C]112.8[/C][C]111.679753778645[/C][C]1.12024622135546[/C][/ROW]
[ROW][C]62[/C][C]128[/C][C]128.050999512433[/C][C]-0.0509995124329651[/C][/ROW]
[ROW][C]63[/C][C]129.6[/C][C]130.108142369576[/C][C]-0.508142369575828[/C][/ROW]
[ROW][C]64[/C][C]125.8[/C][C]123.436713798147[/C][C]2.36328620185275[/C][/ROW]
[ROW][C]65[/C][C]119.5[/C][C]122.39385665529[/C][C]-2.89385665529010[/C][/ROW]
[ROW][C]66[/C][C]115.7[/C][C]116.522428083862[/C][C]-0.822428083861532[/C][/ROW]
[ROW][C]67[/C][C]113.6[/C][C]115.308142369576[/C][C]-1.70814236957582[/C][/ROW]
[ROW][C]68[/C][C]129.7[/C][C]127.122428083862[/C][C]2.57757191613846[/C][/ROW]
[ROW][C]69[/C][C]112[/C][C]118.165285226719[/C][C]-6.16528522671867[/C][/ROW]
[ROW][C]70[/C][C]116.8[/C][C]116.179570941004[/C][C]0.620429058995612[/C][/ROW]
[ROW][C]71[/C][C]127[/C][C]126.665285226719[/C][C]0.334714773281321[/C][/ROW]
[ROW][C]72[/C][C]112.1[/C][C]109.066260360800[/C][C]3.03373963920038[/C][/ROW]
[ROW][C]73[/C][C]114.2[/C][C]111.081472452462[/C][C]3.11852754753782[/C][/ROW]
[ROW][C]74[/C][C]121.1[/C][C]127.452718186251[/C][C]-6.35271818625062[/C][/ROW]
[ROW][C]75[/C][C]131.6[/C][C]129.509861043393[/C][C]2.09013895660653[/C][/ROW]
[ROW][C]76[/C][C]125[/C][C]122.838432471965[/C][C]2.1615675280351[/C][/ROW]
[ROW][C]77[/C][C]120.4[/C][C]121.795575329108[/C][C]-1.39557532910775[/C][/ROW]
[ROW][C]78[/C][C]117.7[/C][C]115.924146757679[/C][C]1.77585324232082[/C][/ROW]
[ROW][C]79[/C][C]117.5[/C][C]114.709861043393[/C][C]2.79013895660653[/C][/ROW]
[ROW][C]80[/C][C]120.6[/C][C]126.524146757679[/C][C]-5.92414675767919[/C][/ROW]
[ROW][C]81[/C][C]127.5[/C][C]117.567003900536[/C][C]9.93299609946367[/C][/ROW]
[ROW][C]82[/C][C]112.3[/C][C]115.581289614822[/C][C]-3.28128961482205[/C][/ROW]
[ROW][C]83[/C][C]124.5[/C][C]126.067003900536[/C][C]-1.56700390053633[/C][/ROW]
[ROW][C]84[/C][C]115.2[/C][C]112.483508044856[/C][C]2.71649195514383[/C][/ROW]
[ROW][C]85[/C][C]105.4[/C][C]114.498720136519[/C][C]-9.09872013651875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25281&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25281&T=4

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	97.8	94.593515358362	3.20648464163802
2	107.4	110.964761092150	-3.56476109215017
3	117.5	113.021903949293	4.47809605070698
4	105.6	106.350475377864	-0.750475377864452
5	97.4	105.307618235007	-7.9076182350073
6	99.5	99.4361896635787	0.0638103364212654
7	98	98.221903949293	-0.221903949293019
8	104.3	110.036189663579	-5.73618966357873
9	100.6	101.079046806436	-0.479046806435882
10	101.1	99.0933325207216	2.00666747927841
11	103.9	109.579046806436	-5.67904680643587
12	96.9	95.9955509507557	0.904449049244283
13	95.5	98.0107630424183	-2.51076304241829
14	108.4	114.382008776207	-5.98200877620671
15	117	116.439151633350	0.560848366650421
16	103.8	109.767723061921	-5.96772306192101
17	100.8	108.724865919064	-7.92486591906387
18	110.6	102.853437347635	7.7465626523647
19	104	101.639151633350	2.36084836665042
20	112.6	113.453437347635	-0.8534373476353
21	107.3	104.496294490492	2.80370550950756
22	98.9	102.510580204778	-3.61058020477815
23	109.8	112.996294490492	-3.19629449049244
24	104.9	99.4127986348123	5.48720136518773
25	102.2	101.428010726475	0.771989273525143
26	123.9	117.799256460263	6.10074353973672
27	124.9	119.856399317406	5.04360068259387
28	112.7	113.184970745978	-0.484970745977566
29	121.9	112.142113603120	9.75788639687958
30	100.6	106.270685031692	-5.67068503169186
31	104.3	105.056399317406	-0.756399317406144
32	120.4	116.870685031692	3.52931496830816
33	107.5	107.913542174549	-0.413542174548996
34	102.9	105.927827888835	-3.02782788883471
35	125.6	116.413542174549	9.186457825451
36	107.5	102.830046318869	4.66995368113116
37	108.8	104.845258410531	3.95474158946858
38	128.4	121.216504144320	7.18349585568016
39	121.1	123.273647001463	-2.17364700146271
40	119.5	116.602218430034	2.89778156996587
41	128.7	115.559361287177	13.140638712823
42	108.7	109.687932715748	-0.987932715748414
43	105.5	108.473647001463	-2.9736470014627
44	119.8	120.287932715748	-0.487932715748415
45	111.3	111.330789858606	-0.0307898586055590
46	110.6	109.345075572891	1.25492442710872
47	120.1	119.830789858606	0.269210141394436
48	97.5	106.247294002925	-8.7472940029254
49	107.7	108.262506094588	-0.562506094587979
50	127.3	124.633751828376	2.66624817162359
51	117.2	126.690894685519	-9.49089468551926
52	119.8	120.019466114091	-0.219466114090695
53	116.2	118.976608971234	-2.77660897123355
54	111	113.105180399805	-2.10518039980498
55	112.4	111.890894685519	0.509105314480739
56	130.6	123.705180399805	6.89481960019502
57	109.1	114.748037542662	-5.64803754266212
58	118.8	112.762323256948	6.03767674305216
59	123.9	123.248037542662	0.651962457337885
60	101.6	109.664541686982	-8.06454168698197
61	112.8	111.679753778645	1.12024622135546
62	128	128.050999512433	-0.0509995124329651
63	129.6	130.108142369576	-0.508142369575828
64	125.8	123.436713798147	2.36328620185275
65	119.5	122.39385665529	-2.89385665529010
66	115.7	116.522428083862	-0.822428083861532
67	113.6	115.308142369576	-1.70814236957582
68	129.7	127.122428083862	2.57757191613846
69	112	118.165285226719	-6.16528522671867
70	116.8	116.179570941004	0.620429058995612
71	127	126.665285226719	0.334714773281321
72	112.1	109.066260360800	3.03373963920038
73	114.2	111.081472452462	3.11852754753782
74	121.1	127.452718186251	-6.35271818625062
75	131.6	129.509861043393	2.09013895660653
76	125	122.838432471965	2.1615675280351
77	120.4	121.795575329108	-1.39557532910775
78	117.7	115.924146757679	1.77585324232082
79	117.5	114.709861043393	2.79013895660653
80	120.6	126.524146757679	-5.92414675767919
81	127.5	117.567003900536	9.93299609946367
82	112.3	115.581289614822	-3.28128961482205
83	124.5	126.067003900536	-1.56700390053633
84	115.2	112.483508044856	2.71649195514383
85	105.4	114.498720136519	-9.09872013651875

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code